For a more challenging version of this game, you could look at Connect Three.

Why dothis problem?

This problem is a great way for students to take responsibility for their own learning. They can avoid negative numbers if they are not confident or they can push themselves to calculate negative answers. In analysing the game more fully, rather than just playing it, the idea is that learners can develop a system
for finding all the possible ways of making each number on the grid, so they can justify which are the easiest to get.

Possible approach

You could introduce the game by playing against the class, or by splitting the class into two teams to play against each other, or with the class playing against the computer. Students can play against each other in pairs to get more of an idea of the game. You can print off this boardif the students are not playing at a computer.

After a suitable length of time, ask the suggested questions in a whole-class discussion that focuses on emerging strategies, observations, explanations and justifications. Students can then go back to working in pairs to establish the numbers of ways of achieving the different totals.

At the end of the lesson a plenary discussion can offer a chance to present findings and you can draw attention to those methods which were particularly efficient. This would then lead to a discussion about how their findings might affect the way they play the game to win.

Key questions

Are there some numbers that we should be aiming for? Why?

Which numbers on the grid are the easiest to get? Why?

Which numbers are most difficult to get? Why?

Possible extension

Further challenges could be provided by asking what would happen if:

there was a differently shaped board

numbers appeared more than once on the board and you could place more than one counter in a turn

you could use dodecahedral dice or, for example, $1-12$ spinners

you wanted to design a board for a game where you allowed multiplication and division